EduSahara™ Worksheet

Question 1

1.

In the given figure, △CDE ∼ △NOP and CD = 13 cm, NO = 18.2 cm.

(i)

126.98 sq.cm
(ii)

128.98 sq.cm
(iii)

127.98 sq.cm
(iv)

124.98 sq.cm
(v)

125.98 sq.cm

Question 2

2.

In the given figure, I and J are points on the sides FG and FH respectively of △FGH.For which of the following cases, IJ ∥ GH

a)	FI = 5 cm, IG = 10 cm, FJ = 5.33 cm and JH = 10.67 cm
b)	FG = 15 cm, IG = 10 cm, FJ = 7.33 cm and FH = 16 cm
c)	FG = 15 cm, FI = 7 cm, FH = 16 cm and JH = 10.67 cm
d)	FG = 15 cm, IG = 10 cm, FH = 16 cm and FJ = 5.33 cm

(i)

{c,d}
(ii)

{b,d,a}
(iii)

{b,c,a}
(iv)

{b,a}
(v)

{a,d}

Question 3

3.

△ABC is a triangle with sides BC = 13 cm, CA = 15 cm and AB = 11 cm. △ABC is enlarged to △A'B'C' such that the smallest side of △A'B'C' is 33 cm. Find the corresponding lengths of the enlarged triangle △A'B'C'.

(i)

37 cm, 43 cm, 31 cm
(ii)

40 cm, 46 cm, 34 cm
(iii)

41 cm, 47 cm, 35 cm
(iv)

39 cm, 45 cm, 33 cm
(v)

38 cm, 44 cm, 32 cm

Question 4

4.

In the given figure, QR ∥ HI , and median GJ bisects QR.
△GHJ ∼

(i)

△GJI
(ii)

△GHI
(iii)

△HIG
(iv)

△GQK
(v)

△GKR

Question 5

5.

Which of the following are true?

a)	Congruent figures have same area.
b)	Similar and congruent are not synonymous.
c)	If two figures are similar, then they are congruent too.
d)	If two figures are congruent, then they are similar too.
e)	Similar figures have same area.

(i)

{c,a}
(ii)

{e,b}
(iii)

{a,b,d}
(iv)

{c,a,b}
(v)

{c,e,d}

Question 6

6.

The perimeters of two similar triangles are 30 cm and 23 cm respectively. If one side of the first triangle is 10 cm, find the length of the corresponding side of the second triangle.

(i)

5.67 cm
(ii)

7.67 cm
(iii)

6.67 cm
(iv)

8.67 cm
(v)

9.67 cm

Question 7

7.

A model of a ship is made to a scale of 1 : 180. If the length of the ship is 1800 m, calculate length of the model ship.

(i)

15.00 m
(ii)

13.00 m
(iii)

7.00 m
(iv)

5.00 m
(v)

10.00 m

Question 8

8.

A triangle having an area 72.62 sq.cm is reduced by a scale factor of 0.44. Find the area of its image.

(i)

11.06 sq.cm
(ii)

17.06 sq.cm
(iii)

19.06 sq.cm
(iv)

9.06 sq.cm
(v)

14.06 sq.cm

Question 9

9.

A model of a ship is made to a scale of 1 : 160. If length of the model ship is 18 m, calculate the length of the ship.

(i)

2880.00 m
(ii)

3150.00 m
(iii)

2720.00 m
(iv)

3020.00 m
(v)

2700.00 m

Question 10

10.

In the given figure, points E , F and G are the mid-points of sides CD, DB and BC of △BCD. Which of the following are true?

a)	△FED ∼ △BCD
b)	△EFG ∼ △BCD
c)	△BGF ∼ △BCD
d)	△EGF ∼ △BCD
e)	△GCE ∼ △BCD

(i)

{d,b}
(ii)

{d,e,a}
(iii)

{a,b,c,e}
(iv)

{d,a}
(v)

{d,c}

Question 11

11.

BCDE is a cyclic trapezium. Diagonals CE and BD intersect at F. If EB = 16 cm, find CD

(i)

17 cm
(ii)

18 cm
(iii)

14 cm
(iv)

15 cm
(v)

16 cm

Question 12

12.

In the given figure,
HI
∥
FG
.

(i)

3.80 cm
(ii)

2.80 cm
(iii)

5.80 cm
(iv)

6.80 cm
(v)

4.80 cm

Question 13

13.

In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 26 cm and AP = 10 cm. Find PB

(i)

16.00 cm
(ii)

17.00 cm
(iii)

15.00 cm
(iv)

18.00 cm
(v)

14.00 cm

Question 14

14.

In the given figure, given ∠FCD = ∠ECF, x : y = 8.73 cm : 7.27 cm and q = 15 cm, find p =

(i)

19.00 cm
(ii)

17.00 cm
(iii)

18.00 cm
(iv)

20.00 cm
(v)

16.00 cm

Question 15

15.

The measurements of a triangular field △ABC are BC = 5 cm, AB = 11 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 15000. Calculate the actual area of the plot in sq.km.

(i)

0.62 sq.km
(ii)

8.62 sq.km
(iii)

1.62 sq.km
(iv)

7.62 sq.km
(v)

2.62 sq.km

Question 16

16.

Which of the following are true?

a)	Area of the union of two polygonal region is the sum of the individual area.
b)	A polygonal region can be divided into a finite number of triangles in a unique way.
c)	Area of a convex polygonal region is equal to the sum of the areas of all triangles formed by joining the vertices of the polygon with an interior point.
d)	Area of the union of two polygonal region is not equal to the sum of the individual area.

(i)

{a,b,c}
(ii)

{c,d}
(iii)

{b,d}
(iv)

{a,c}
(v)

{a,d,c}

Question 17

17.

In the given △EFG, HI ∥ FG. If EH : HF = 12 cm : 6 cm and EG = 20 cm, EI =

(i)

15.33 cm
(ii)

11.33 cm
(iii)

13.33 cm
(iv)

14.33 cm
(v)

12.33 cm

Question 18

18.

In the given figure, the area of the △IJK is x sq.cm. L,M,N are the mid-points of the sides JK , KI and IJ respectively. The area of the △LMN is

(i)
3
4

of area of △IJK
(ii)
1
3

of area of △IJK
(iii)
2
3

of area of △IJK
(iv)
1
2

of area of △IJK
(v)
1
4

of area of △IJK

Question 19

19.

In the given figure, if HI ∥ JK then

(i)

△LHI ∼ △LJK
(ii)

△HIL ∼ △LKJ
(iii)

△HIL ∼ △LJK
(iv)

△LIH ∼ △LKJ
(v)

△HIL ∼ △KJL

Question 20

20.

A rectangle having an area 60.00 sq.cm is reduced by a scale factor of 0.89. Find the area of its image.

(i)

47.53 sq.cm
(ii)

44.53 sq.cm
(iii)

52.53 sq.cm
(iv)

42.53 sq.cm
(v)

50.53 sq.cm

Question 21

21.

If the ratio of the bases of two triangles is K : L and the ratio of the corresponding heights is M : N , the ratio of their areas in the same order is

(i)

KL : MN
(ii)

MN : KL
(iii)

KN : LM
(iv)

LM : KN
(v)

KM : LN

Question 22

22.

In the given figure, the two circles touch each other internally.

Diameter
OB
passes through the centre of the smaller circle.

Find the radius of the outer circle.

(i)

13.00 cm
(ii)

10.00 cm
(iii)

11.00 cm
(iv)

14.00 cm
(v)

12.00 cm

Question 23

23.

In the given figure, △EFG is right-angled at F. Also, FH ⟂ EG. If FG = 17 cm, FH = 11.25 cm, then find EF.

(i)

14.00 cm
(ii)

13.00 cm
(iii)

17.00 cm
(iv)

16.00 cm
(v)

15.00 cm

Question 24

24.

In the given figure, QR ∥ BC and AQ = 13.2 cm, AB = 22 cm and QR = 12 cm, find BC

(i)

20.0 cm
(ii)

18.0 cm
(iii)

22.0 cm
(iv)

21.0 cm
(v)

19.0 cm

Question 25

25.

A model of a ship is made to a scale of 1 : 65. If the area of the deck of the ship is 1368900 sq.m, calculate the area of the deck of the model ship.

(i)

324.00 sq.m
(ii)

336.00 sq.m
(iii)

352.00 sq.m
(iv)

311.00 sq.m
(v)

309.00 sq.m

Assignment Key